Market press products in multiple categories

Hi, I have a situation with products where I want to have a single product multiple attributes so the user can reach them via a different route in the sidebar navigation.

So a made up example would be

Top level - Cleaning Tools
Second Level - Broom
Third level attribute - Long Handled
Third level attribute - Short Handled
Second Level - Mop
Third level attribute - Long Handled
Third level attribute - Short Handled

So you can see there are Long Handled Mops and Long Handled Brooms

The situation I want to get to is via some form of 'navigation' (without resorting to serach) the user can select Long Handle and then get Brooms and Mops and then drill down, or the User can select Mops and then drill down to Long or Short Handled Mops.

The issue I have, is with out of the box categories and navigation, if I apply the product to multiple categories then if they select Mops they will get all Long & Short, but then if they select Long, it will give both Mops and Brushes as there is no drill down concept.

I also though about using tags as an alternative category, but teh lack of drill down still occurs.

If I create Mops -> Long Handled Mops
Brooms -> Long Handled Brooms
I would need to create all permutations of top and next level,
Mops -> Short
Brooms -> Short
Short - > Brooms
Short -> Mops
Long -> Brooms
Long -> Mops
which would create a massive number of navigation items (if would be some sort of permutation so easily could become unmanageable, with more than two alternative categories).

This sort of 'drill down' through product categories is a common e-commerce situation. And being Wordpress, others must have solved this problem many times.

Can you give me any ideas, pointers to plugins that might be adaptable etc. to get a better solution.